How to add a texture to a section that is already a part of a larger object with one?
First the odd thing. I don't know the origin of your model, but every mesh of your model has a copy, that can be identified by the .001 extension in the Outliner. This does make things very confusing, so I'm going to work on the copy while the original will be hidden. 



Analyzing the Mesh

As I expected, your model is divided into several meshes, with each of them containing sub-meshes. These sub-meshes don't share vertices so they can easily selected in Edit Mode by clicking on one of the vertices and then expand the selection by hitting Ctrl+Numpad + until the whole sub-mesh is selected. 



After selecting the hair mesh, we see the UV layout in the UV/Image Editor. Let's keep it as it is. We also recognize the name of the currently assigned texture, which is faceoff.png. We also have a material in the material editor that goes by the same name, so let's keep this convention. 



Preparing and assigning the Material

If we click on the image selector in the UV/Image Editor we find an image named s76_hair.png. 



Now we create a new material named s76_hair and assign the right texture to a new slot. (Texture names aren't necessarily file names, I chose the first one that matches the UV I looked up in the image editor - in this case it's Texture.006). To play it safe, we also assign the UV map for the correct mapping.



In the last step we assign the material to the hair mesh. With the hair mesh still selected, we go to the Material Editor, select our newly created material and hit "Assign".



If we look at our model in Texture Paint mode, we'll see that now the correct texture shows on the mesh.